U.S. Pat. Nos. 5,552,003 and 5,693,163 respectively entitled “Method for Producing Inflated Dunnage” and “Inflated Dunnage and Method for Its Production” and respectively issued Sep. 3, 1996 and Dec. 2, 1997 to Gregory k Hoover et al. (the Dunnage Patents) disclose a method for producing dunnage utilizing preopened bags on a roll. The preopened bags utilized in the Dunnage Patents are of a type disclosed in U.S. Pat. No. 3,254,828 issued Jun. 2, 1996 to Hershey Lerner and entitled “Flexible Container Strips” (the “Autobag Patent”). The preferred bags of the Dunnage Patents are unique in that the so-called tack of outer bag surfaces is greater than the tack of inner surfaces to facilitate bag opening while producing dunnage units which stick to one another when in use.